Floor plan revision, tips and experiences for improvement?

On the topic of converting one house into two apartments:

Two adults, 40 years old, two children, 11 and 13 years old

Give some thought to the way of life.
In 15 years, the children will be 26 and 28 years old, you will be 55. The children will be in training or finished. They will go their own way, whether alone or with a partner, near or far.
One child needs an apartment, with a partner it would be rather cramped, so only an emergency solution.
You are 55 and even earlier, when the kids move out, then exactly at the age to enjoy the house without children, with the advantages of having two rooms (so only 2 rooms) free to use. Sleeping separately or additionally as a hobby room.
One does not want to use a house only on one level, without a dressing room and with a guest toilet.
Let’s assume one child has not managed their own living comfort at 35. You will then be only 62, still working, settled in life, then the same applies: you do not want to restrict yourself yet, and you don’t have to. Grandchildren have a former children’s room to stay overnight.
In 30 years you will be 70, but here too: golden years, you enjoy your own house with the advantages. Grandchildren no longer come as overnight guests because of lack of interest, but you enjoy your free space, maybe you think about a caregiver, who could take over a former children’s room. Maybe by now you need physiotherapy equipment, which is also well accommodated.
Maybe you already know now that one child must stay because they are limited. But then these facts belong in the original thread, that is, in the questionnaire, because they are indirectly inquired there. So let’s assume no child will be needy later.

If you consider this and keep in mind that possibly the partner would also not move under the roof of the parents-in-law, but you are afraid that the house will become too big in the long run, what remains?
Perhaps the idea to plan the multi/office/guest room immediately as a proper master bedroom with an adequate shower bath on the upper floor and also to live in it in such a way that you do not have to restrict yourself later.
Downstairs the children with a study, a second (children’s) bathroom, so that as “old parents” you can spread out there as mentioned above, and much later then actually a caregiver moves in downstairs, with adequate rooms without family bathroom, but compact.
What remains as an option: of course selling a house that is too big and moving into something more compact for an older couple, without a slope, stairs and useless rooms.

Would you rather position the house so that the lower floor is fully embedded at the back and we would then have to rearrange our floor plan, but [...] to get to the garden on the north side via the stairs at the roof terrace?
[ / ] We cannot plan a sensible granny flat like this,

The floor plan should not be "rearranged" but conceptually redeveloped (and by an architect - not by a "designer")!
You keep asking such questions as if you want to participate in this concept. You should, but in the form of lists with requirements and wishes. A lawyer who represents himself has a fool for a client - this applies just as well to prospective homeowners. Laypeople should only try to contribute visually to a building planning at the earliest for their second house (and even later for a slope site), otherwise their overconfidence will hurt them badly. If you want to save on the architect, you will pay dearly — at least twice his fee (for both halves!) — do you have that much money to spare?

One more storey increases the house building costs enormously and creates space we do not want. We would like only what is really needed and everything can fit on two storeys. The plot suits our ideas for two living units well; that claim is nonsense. More useful for us would be tips on where to position which room in the basement, or, as described above, how to model the terrain. I can work with that, thanks for that.

The building costs depend on creating space in the right measure. That automatically produces the right building form (unless a layperson wants to tamper with it themselves). Terrain modelling increases building costs enormously and is precisely avoided by the right building form conception. Leaving the allocation of the room program to the architect. The soon-to-be teenagers I would accommodate in a unit consisting of two children's rooms, a children's bathroom, and a corridor with an external entrance and later lockable access to the main dwelling, which I would design in the basement and from the start as a granny flat. By the way, building services can quite well go into the roof; downwards and close to the street is only important for house connections. This also makes the house most attractive for resale. Terrace and garden on different levels are unrealistic and should be avoided. Nevertheless, I would consider a viewing terrace (caution: leave a building line free!) on the garage roof here.

Nevertheless, I would consider a viewing terrace here (Caution: leave building setback free!) on the garage roof.

Why nevertheless? That is originally and generally planned. Or do you mean the other nevertheless?

Why nevertheless? That is originally and generally planned.
Or do you mean something else nevertheless?

I do not know of two kinds of nevertheless. My nevertheless refers to the fact that in the sentence before I said not to distribute terrace and garden on separate levels. But for enjoying the view, it may be nice to have a platform. The roof of the garage would be suitable for that. Of course, I am talking about a garage that, according to my suggestion, stands separated from the main building. Originally planned is a roof terrace on the garage connected to the house (which I at least advise against prioritizing highly and instead recommend to exclude it from the calculation of level distribution). Yes, in the original plan the building setback would be respected, but I am precisely advising not to continue pursuing that, but to consistently discard it.